Zero Padding

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Definition:Zero
padding consists of
appending zeros to a signal. It maps a length signal to
a length
signal, but need
not be an integer multiple of :

For example,

The above definition is natural when
represents a signal starting at time and
extending for
samples. If, on the other hand, we are zero-padding a spectrum, or
we have a time-domain signal which has nonzero samples for negative
time indices, then the zero padding is normally inserted between
samples
and
for odd (note
that ), and
similarly for even . I.e., for spectra, zero padding is inserted at the point
(
). Figure 8.5
illustrates this second form of zero padding. It is also used in
conjunction with zero-phase FFT
windows(discussed a bit further below).

Figure 8.5:Illustration of
frequency-domain
zero padding: a) Original spectrum plotted over the domain
where (i.e.,
as the spectral array would normally exist in a computer array). b)
. c) The same signal plotted
over the domain which is more natural for interpreting
negative frequencies. d) .